Relationship between wintering latitude and arrival/departure timings of migratory birds
Karthik Thrikkadeeri
2024/08/15
Introduction
- Relationship between migration timings and latitude has received some attention, such as: In breeding ranges, how does latitude influence the migrant proportion of bird populations? i.e. whether or not a breeding bird migrates south.
- Studies on when migration occurs:
- Either on effect of breeding latitudes
- Various other env. variables affect migration timing, and how this changes with climate change Gordo et al. (2005)
- Or asking how wintering latitudes affect timing of arrival in breeding grounds
- Species wintering in higher/temperate latitudes migrate (arrive in breeding range) earlier than tropical wintering ones. Breeding latitude does not have an effect. (Hagan et al. 1991)
- Synchronicity of migration itself has received very little attention
- But from Hagan et al. (1991) we can retain the notion of synchronicity. According to those findings, the greater the latitudinal range occupied by a species in winter, the more asynchronous its migration will be.
- The reality, and what we can see in our prelim explorations, is a bit more complex than that, of course. Not a linear relationship.
- But what exactly is the relationship between migration timings (special focus on synchronicity) and wintering latitudes (minima, median, breadth)? And what does the relationship imply ecologically?
- Also related to Zugunruhe, as suggested for Phylloscopus (Åkesson et al. 2017)
- Longer-distance migrants more synchronous (Winger et al. 2024)
Most migration studies heavily physiological, while our aim with this is more functional (traits-based). Macroecological perspective on seasonal flux of animal movement (different from tracking studies), allowing cross-species comparisons of broad-scale strategies in pace and geography of annual cycle stages.
We also have certain species whose entire global population winters in India (e.g., Blyth’s Reed Warbler, Greenish Warbler). This is a good opportunity to gain understandings of global ecological (and conservation) significance.
Questions
- Cross-species comparisons:
- Does winter arrival/departure timing depend on the species’s wintering latitude?
- Does winter migration synchronicity depend on the species’s wintering latitude?
- Do species migrating later in season tend to migrate more synchronously?
- Is winter arrival/departure timing changing over the years (climate change)?
- As a final section, if relevant and feasible (low data, quantile method might fail.).
- Or, instead can maybe try to correlate with temperature gradient across latitudes to speculate.
- Within-species comparisons:
- Do species follow same synchronicity strategy for arrival and departure? (Symmetricity, see Winger et al. (2024))
- Which do, and which don’t (what determines this)?
- Is synchronicity more likely/common in arrival than in departure or vice-versa?
- Many species have narrower window in spring than in fall (Winger et al. 2024 for references)
- In India (maybe unique) we have monsoon, so most species probably spend longer coming down due to availability of food in post-monsoon
- Do species follow same synchronicity strategy for arrival and departure? (Symmetricity, see Winger et al. (2024))
Northwest vs Himalayan routes
Metrics:
- Migration timing:
- True arrival/departure, not absolute (stragglers)
- Synchronicity
- Wintering latitude:
- Minimum
- Median
- Extent/breadth/range
Exploration (methods)
For high-res versions of images, go here.
Investigating arrival and departure timings & synchronicity
After all our selection and filtering criteria for wintering species of interest (giving 90 species), and after filtering data for each species to its wintering latitudinal range (removing latitudes where not purely wintering), we now start the analysis.
Using quantiles (assuming 95%), we determine “true” arrival and departure dates for each species per latitude. For a preliminary visualisation of patterns across species, we visualise this latitudinal trend of arrival (blue) & departure (red) times for all species:
Figure 1: True arrival and departure timings of our wintering species, using the quantile method.
Figure 2: True arrival and departure timings of our wintering species, using the quantile method.
We now calculate metrics for migration timings, such as first northern/southern arrival & departure, and synchronicity which is our primary metric of interest. We describe synchronicity using two (presumably) orthogonal angles: slope (quickness of migration) and tightness (uniformity) across latitudes. (Correlation R^2 cannot be used for the measure of tightness, since for high slope values, R2 becomes low.)
Here are the synchronicity measures (SYNC.SLOPE & SYNC.TIGHT) for a set of illustrative species, followed by updated plots for the same species.
## # A tibble: 50 × 6
## COMMON.NAME DATE.TYPE SLOPE SE SYNC.SLOPE SYNC.TIGHT
## <chr> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 Cinereous Vulture DEP 6.21 0.921 -1.60 0.0827
## 2 Bar-tailed Godwit DEP 3.89 2.60 -1.19 -0.956
## 3 Brown-breasted Flycatcher DEP 2.47 0.479 -0.795 0.737
## 4 Black Redstart DEP 2.21 0.292 -0.696 1.23
## 5 Blyth's Reed Warbler DEP 1.86 0.213 -0.548 1.55
## 6 Red-breasted Flycatcher DEP 1.53 0.312 -0.373 1.16
## 7 Lesser Whitethroat DEP 1.50 0.462 -0.361 0.771
## 8 Common Chiffchaff DEP 1.46 0.410 -0.332 0.891
## 9 Siberian Stonechat DEP 1.39 0.246 -0.293 1.40
## 10 Bar-headed Goose DEP 1.26 0.283 -0.203 1.26
## 11 Taiga Flycatcher DEP 0.988 0.300 0.00665 1.21
## 12 Eurasian Wigeon DEP 0.795 0.344 0.197 1.07
## 13 Brown-headed Gull DEP -0.766 0.472 0.229 0.750
## 14 Brown Shrike DEP 0.519 0.282 0.570 1.27
## 15 Tufted Duck DEP 0.511 0.447 0.584 0.806
## 16 Spotted Redshank DEP 0.504 0.327 0.595 1.12
## 17 Greenish Warbler DEP -0.459 0.362 0.677 1.02
## 18 Gray Wagtail DEP 0.425 0.253 0.745 1.38
## 19 Green Warbler DEP 0.363 0.467 0.883 0.762
## 20 Common Buzzard DEP -0.272 0.880 1.13 0.128
## 21 Greater Spotted Eagle DEP 0.245 0.254 1.23 1.37
## 22 Sykes's Warbler DEP 0.147 0.847 1.67 0.166
## 23 Western Yellow Wagtail DEP 0.0612 0.241 2.44 1.42
## 24 Booted Eagle DEP -0.0444 0.250 2.72 1.39
## 25 Pallid Harrier DEP 0.0227 0.334 3.31 1.10
## 26 Blyth's Reed Warbler ARR -3.33 0.459 -1.06 0.778
## 27 Cinereous Vulture ARR -2.39 2.38 -0.766 -0.866
## 28 Green Warbler ARR -1.78 0.270 -0.510 1.31
## 29 Brown-breasted Flycatcher ARR -1.78 1.02 -0.506 -0.0229
## 30 Western Yellow Wagtail ARR -1.73 0.204 -0.481 1.59
## 31 Pallid Harrier ARR -1.62 0.240 -0.423 1.43
## 32 Sykes's Warbler ARR -1.51 0.984 -0.362 0.0157
## 33 Eurasian Wigeon ARR -1.35 0.272 -0.266 1.30
## 34 Common Chiffchaff ARR -1.22 0.440 -0.176 0.821
## 35 Brown-headed Gull ARR -1.04 0.533 -0.0368 0.630
## 36 Bar-tailed Godwit ARR -0.997 0.958 -0.000733 0.0428
## 37 Greenish Warbler ARR -0.980 0.280 0.0143 1.27
## 38 Booted Eagle ARR -0.976 0.209 0.0177 1.57
## 39 Brown Shrike ARR -0.732 0.160 0.270 1.83
## 40 Taiga Flycatcher ARR -0.722 0.250 0.281 1.39
## 41 Siberian Stonechat ARR -0.705 0.182 0.302 1.70
## 42 Tufted Duck ARR -0.700 0.527 0.308 0.640
## 43 Red-breasted Flycatcher ARR -0.642 0.248 0.384 1.39
## 44 Lesser Whitethroat ARR -0.610 0.255 0.429 1.36
## 45 Spotted Redshank ARR 0.552 1.02 0.516 -0.0168
## 46 Common Buzzard ARR 0.480 0.335 0.637 1.09
## 47 Black Redstart ARR -0.409 0.172 0.779 1.76
## 48 Gray Wagtail ARR 0.342 0.209 0.934 1.57
## 49 Bar-headed Goose ARR -0.129 0.146 1.79 1.92
## 50 Greater Spotted Eagle ARR 0.0515 0.332 2.59 1.10
Figure 3: Set of illustrative species arranged in order of synchronicity of arrival/departure.
Figure 4: Set of illustrative species arranged in order of synchronicity of arrival/departure.
All our species can be visualised as occupying a 2-D space governed by the two measures of synchronicity. Based on their occupancy of this space, we can classify their overall synchronicity.
Figure 5: 2D space of synchronicity measures of our species.
Now will try to combine the two variables into a single index of synchronicity. Relative weights are obtained from PCA of the two variables, and the index (SYNC.IND) is a linear combination of the two. New values and updated graphs below.
## # A tibble: 50 × 5
## COMMON.NAME DATE.TYPE SYNC.SLOPE SYNC.TIGHT SYNC.IND
## <chr> <fct> <dbl> <dbl> <dbl>
## 1 Bar-tailed Godwit DEP -1.19 -0.956 -1.12
## 2 Cinereous Vulture DEP -1.60 0.0827 -1.08
## 3 Brown-breasted Flycatcher DEP -0.795 0.737 -0.320
## 4 Black Redstart DEP -0.696 1.23 -0.0982
## 5 Lesser Whitethroat DEP -0.361 0.771 -0.00962
## 6 Common Chiffchaff DEP -0.332 0.891 0.0472
## 7 Blyth's Reed Warbler DEP -0.548 1.55 0.102
## 8 Red-breasted Flycatcher DEP -0.373 1.16 0.103
## 9 Siberian Stonechat DEP -0.293 1.40 0.233
## 10 Bar-headed Goose DEP -0.203 1.26 0.252
## 11 Taiga Flycatcher DEP 0.00665 1.21 0.378
## 12 Brown-headed Gull DEP 0.229 0.750 0.391
## 13 Eurasian Wigeon DEP 0.197 1.07 0.466
## 14 Tufted Duck DEP 0.584 0.806 0.653
## 15 Spotted Redshank DEP 0.595 1.12 0.757
## 16 Greenish Warbler DEP 0.677 1.02 0.782
## 17 Brown Shrike DEP 0.570 1.27 0.786
## 18 Common Buzzard DEP 1.13 0.128 0.822
## 19 Green Warbler DEP 0.883 0.762 0.846
## 20 Gray Wagtail DEP 0.745 1.38 0.940
## 21 Sykes's Warbler DEP 1.67 0.166 1.21
## 22 Greater Spotted Eagle DEP 1.23 1.37 1.27
## 23 Western Yellow Wagtail DEP 2.44 1.42 2.13
## 24 Booted Eagle DEP 2.72 1.39 2.31
## 25 Pallid Harrier DEP 3.31 1.10 2.62
## 26 Cinereous Vulture ARR -0.766 -0.866 -0.797
## 27 Blyth's Reed Warbler ARR -1.06 0.778 -0.487
## 28 Brown-breasted Flycatcher ARR -0.506 -0.0229 -0.357
## 29 Sykes's Warbler ARR -0.362 0.0157 -0.245
## 30 Bar-tailed Godwit ARR -0.000733 0.0428 0.0127
## 31 Green Warbler ARR -0.510 1.31 0.0545
## 32 Common Chiffchaff ARR -0.176 0.821 0.133
## 33 Pallid Harrier ARR -0.423 1.43 0.151
## 34 Western Yellow Wagtail ARR -0.481 1.59 0.160
## 35 Brown-headed Gull ARR -0.0368 0.630 0.170
## 36 Eurasian Wigeon ARR -0.266 1.30 0.220
## 37 Spotted Redshank ARR 0.516 -0.0168 0.351
## 38 Greenish Warbler ARR 0.0143 1.27 0.405
## 39 Tufted Duck ARR 0.308 0.640 0.411
## 40 Booted Eagle ARR 0.0177 1.57 0.498
## 41 Taiga Flycatcher ARR 0.281 1.39 0.624
## 42 Red-breasted Flycatcher ARR 0.384 1.39 0.697
## 43 Lesser Whitethroat ARR 0.429 1.36 0.719
## 44 Siberian Stonechat ARR 0.302 1.70 0.736
## 45 Brown Shrike ARR 0.270 1.83 0.754
## 46 Common Buzzard ARR 0.637 1.09 0.779
## 47 Black Redstart ARR 0.779 1.76 1.08
## 48 Gray Wagtail ARR 0.934 1.57 1.13
## 49 Bar-headed Goose ARR 1.79 1.92 1.83
## 50 Greater Spotted Eagle ARR 2.59 1.10 2.13Figure 6: Species arranged in order of combination of two synchronicity measures.
Figure 7: Species arranged in order of combination of two synchronicity measures.
Clearly, there is still some finetuning to be done with the “quickness” metric, i.e., derived from slope. For the most synchronous species with little difference between them, the values are drastically different. Also need to figure out how to appropriately weight the two so that high togetherness is prioritised.
Further try ordinations to understand what factors (wintering, migrating) determine synchronicity of species.
Finalise synchronicity
On discussing with AV, we realised that the second aspect, “tightness” is better viewed as noise rather than information. Even if it appears to have ecological meaning, this is only true for high tightness values and here the information is mostly just from the first metric. So, instead of trying to combine the two aspects, better to ignore species with tightness lower than some threshold value. Consider that low tightness can either be just noise in data, or lack of a strong north-south migration signal in the species, and we can’t tease apart the two (and not of interest in this study; though might still be an orthogonal aspect of synchronicity). So, changes applied:
- Set threshold for variability (tightness) along slope, exclude species above this from our main regression tests with latitude
- With all species (including those excluded above), we divide synchronicity into N bins (think X axis of Fig. 5) and within each bin show how variability (signal) can range from low to high. e.g., highly staggered species can range from BRW (very strong migration signal) to CiVu (less strong signal); very synchronous species can range from BHGo to SpRedshank.
- So now our measure of synchronicity is much simplified: there is only one metric, and that too can be simply the slope from the LM (without any transformations).
- LM seems the best bet here; I did try GLM but the slope there is not the information we want
- Also, LM estimates with and without scaling the DAY.MY to start from 0 (for each species and arrival/departure combo) were the same, so leave it unscaled. See below.
## # A tibble: 5 × 8
## COMMON.NAME DATE.TYPE LM.SLOPE LM.SE SCALED.LM.SLOPE SCALED.LM.SE GLM.SLOPE
## <chr> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Black-capped … ARR -2.11 2.87 -2.11 2.87 0.979
## 2 Black-naped O… ARR 2.78 1.47 2.78 1.47 1.03
## 3 Black-throate… ARR -3.67 1.39 -3.67 1.39 0.876
## 4 Common Pochard ARR 0.0714 1.06 0.0714 1.06 1.00
## 5 Eurasian Grif… ARR -0.514 2.05 -0.514 2.05 0.942
## # ℹ 1 more variable: GLM.SE <dbl>Arranging in order of new synchronicity index (slope of LM):
## # A tibble: 50 × 4
## COMMON.NAME DATE.TYPE SYNC.IND SE
## <chr> <fct> <dbl> <dbl>
## 1 Brown-headed Gull DEP -0.766 0.472
## 2 Greenish Warbler DEP -0.459 0.362
## 3 Common Buzzard DEP -0.272 0.880
## 4 Booted Eagle DEP -0.0444 0.250
## 5 Pallid Harrier DEP 0.0227 0.334
## 6 Western Yellow Wagtail DEP 0.0612 0.241
## 7 Sykes's Warbler DEP 0.147 0.847
## 8 Greater Spotted Eagle DEP 0.245 0.254
## 9 Green Warbler DEP 0.363 0.467
## 10 Gray Wagtail DEP 0.425 0.253
## 11 Spotted Redshank DEP 0.504 0.327
## 12 Tufted Duck DEP 0.511 0.447
## 13 Brown Shrike DEP 0.519 0.282
## 14 Eurasian Wigeon DEP 0.795 0.344
## 15 Taiga Flycatcher DEP 0.988 0.300
## 16 Bar-headed Goose DEP 1.26 0.283
## 17 Siberian Stonechat DEP 1.39 0.246
## 18 Common Chiffchaff DEP 1.46 0.410
## 19 Lesser Whitethroat DEP 1.50 0.462
## 20 Red-breasted Flycatcher DEP 1.53 0.312
## 21 Blyth's Reed Warbler DEP 1.86 0.213
## 22 Black Redstart DEP 2.21 0.292
## 23 Brown-breasted Flycatcher DEP 2.47 0.479
## 24 Bar-tailed Godwit DEP 3.89 2.60
## 25 Cinereous Vulture DEP 6.21 0.921
## 26 Blyth's Reed Warbler ARR -3.33 0.459
## 27 Cinereous Vulture ARR -2.39 2.38
## 28 Green Warbler ARR -1.78 0.270
## 29 Brown-breasted Flycatcher ARR -1.78 1.02
## 30 Western Yellow Wagtail ARR -1.73 0.204
## 31 Pallid Harrier ARR -1.62 0.240
## 32 Sykes's Warbler ARR -1.51 0.984
## 33 Eurasian Wigeon ARR -1.35 0.272
## 34 Common Chiffchaff ARR -1.22 0.440
## 35 Brown-headed Gull ARR -1.04 0.533
## 36 Bar-tailed Godwit ARR -0.997 0.958
## 37 Greenish Warbler ARR -0.980 0.280
## 38 Booted Eagle ARR -0.976 0.209
## 39 Brown Shrike ARR -0.732 0.160
## 40 Taiga Flycatcher ARR -0.722 0.250
## 41 Siberian Stonechat ARR -0.705 0.182
## 42 Tufted Duck ARR -0.700 0.527
## 43 Red-breasted Flycatcher ARR -0.642 0.248
## 44 Lesser Whitethroat ARR -0.610 0.255
## 45 Black Redstart ARR -0.409 0.172
## 46 Bar-headed Goose ARR -0.129 0.146
## 47 Greater Spotted Eagle ARR 0.0515 0.332
## 48 Gray Wagtail ARR 0.342 0.209
## 49 Common Buzzard ARR 0.480 0.335
## 50 Spotted Redshank ARR 0.552 1.02
Figure 8: Species arranged in order of synchronicity (slope).
Figure 9: Species arranged in order of synchronicity (slope).
Determining threshold cutoff for variability (tightness)
This is not very straightforward. Here is a summary of some select species and various measures of theirs (R-squared, residual standard error, degrees of freedom, F statistic, root mean square error, mean absolute error, coefficient of variation).
## # A tibble: 50 × 11
## COMMON.NAME DATE.TYPE SLOPE SE R2 RSE DF F.STAT RMSE MAE
## <chr> <fct> <dbl> <dbl> <dbl> <dbl> <int> <dbl> <dbl> <dbl>
## 1 Bar-headed G… DEP 1.26 0.283 4.73e-1 9.58 22 1.97e+1 9.17 7.31
## 2 Bar-headed G… ARR -0.129 0.146 3.41e-2 4.95 22 7.77e-1 4.74 3.83
## 3 Bar-tailed G… DEP 3.89 2.60 2.71e-1 22.6 6 2.24e+0 19.6 14.7
## 4 Bar-tailed G… ARR -0.997 0.958 1.53e-1 8.33 6 1.08e+0 7.21 5.37
## 5 Black Redsta… DEP 2.21 0.292 7.82e-1 6.72 16 5.73e+1 6.34 5.27
## 6 Black Redsta… ARR -0.409 0.172 2.61e-1 3.96 16 5.65e+0 3.74 2.90
## 7 Blyth's Reed… DEP 1.86 0.213 7.78e-1 7.21 22 7.70e+1 6.90 5.77
## 8 Blyth's Reed… ARR -3.33 0.459 7.05e-1 15.6 22 5.25e+1 14.9 11.0
## 9 Booted Eagle DEP -0.0444 0.250 1.74e-3 6.45 18 3.14e-2 6.12 4.95
## 10 Booted Eagle ARR -0.976 0.209 5.48e-1 5.38 18 2.19e+1 5.11 3.69
## 11 Brown Shrike DEP 0.519 0.282 1.34e-1 9.55 22 3.40e+0 9.14 6.49
## 12 Brown Shrike ARR -0.732 0.160 4.88e-1 5.42 22 2.10e+1 5.19 3.77
## 13 Brown-breast… DEP 2.47 0.479 7.08e-1 7.30 11 2.67e+1 6.72 5.03
## 14 Brown-breast… ARR -1.78 1.02 2.15e-1 15.6 11 3.02e+0 14.4 8.60
## 15 Brown-headed… DEP -0.766 0.472 1.41e-1 13.2 16 2.63e+0 12.5 9.69
## 16 Brown-headed… ARR -1.04 0.533 1.92e-1 14.9 16 3.80e+0 14.1 10.6
## 17 Cinereous Vu… DEP 6.21 0.921 8.35e-1 10.5 9 4.55e+1 9.48 8.07
## 18 Cinereous Vu… ARR -2.39 2.38 1.01e-1 27.1 9 1.01e+0 24.5 17.6
## 19 Common Buzza… DEP -0.272 0.880 6.79e-3 21.2 14 9.58e-2 19.9 14.1
## 20 Common Buzza… ARR 0.480 0.335 1.28e-1 8.08 14 2.06e+0 7.56 5.58
## 21 Common Chiff… DEP 1.46 0.410 4.57e-1 8.28 15 1.26e+1 7.78 6.10
## 22 Common Chiff… ARR -1.22 0.440 3.38e-1 8.88 15 7.67e+0 8.34 6.35
## 23 Eurasian Wig… DEP 0.795 0.344 1.95e-1 12.4 22 5.33e+0 11.9 8.88
## 24 Eurasian Wig… ARR -1.35 0.272 5.27e-1 9.81 22 2.45e+1 9.39 7.30
## 25 Gray Wagtail DEP 0.425 0.253 1.36e-1 6.52 18 2.82e+0 6.18 5.05
## 26 Gray Wagtail ARR 0.342 0.209 1.30e-1 5.38 18 2.69e+0 5.10 4.07
## 27 Greater Spot… DEP 0.245 0.254 3.87e-2 9.16 23 9.27e-1 8.79 6.80
## 28 Greater Spot… ARR 0.0515 0.332 1.04e-3 12.0 23 2.40e-2 11.5 8.01
## 29 Green Warbler DEP 0.363 0.467 3.87e-2 9.43 15 6.04e-1 8.86 7.02
## 30 Green Warbler ARR -1.78 0.270 7.45e-1 5.44 15 4.38e+1 5.11 3.92
## 31 Greenish War… DEP -0.459 0.362 7.45e-2 10.8 20 1.61e+0 10.3 8.83
## 32 Greenish War… ARR -0.980 0.280 3.80e-1 8.32 20 1.23e+1 7.94 6.29
## 33 Lesser White… DEP 1.50 0.462 3.35e-1 14.7 21 1.06e+1 14.1 10.9
## 34 Lesser White… ARR -0.610 0.255 2.13e-1 8.13 21 5.70e+0 7.76 6.39
## 35 Pallid Harri… DEP 0.0227 0.334 2.56e-4 8.96 18 4.60e-3 8.50 7.00
## 36 Pallid Harri… ARR -1.62 0.240 7.16e-1 6.43 18 4.53e+1 6.10 5.03
## 37 Red-breasted… DEP 1.53 0.312 5.45e-1 9.28 20 2.39e+1 8.85 6.69
## 38 Red-breasted… ARR -0.642 0.248 2.50e-1 7.39 20 6.68e+0 7.05 6.05
## 39 Siberian Sto… DEP 1.39 0.246 6.67e-1 5.86 16 3.21e+1 5.52 4.50
## 40 Siberian Sto… ARR -0.705 0.182 4.83e-1 4.35 16 1.49e+1 4.10 3.04
## 41 Spotted Reds… DEP 0.504 0.327 1.16e-1 9.96 18 2.37e+0 9.45 7.35
## 42 Spotted Reds… ARR 0.552 1.02 1.61e-2 30.9 18 2.94e-1 29.4 22.4
## 43 Sykes's Warb… DEP 0.147 0.847 2.00e-3 18.5 15 3.01e-2 17.3 13.1
## 44 Sykes's Warb… ARR -1.51 0.984 1.35e-1 21.5 15 2.34e+0 20.2 17.3
## 45 Taiga Flycat… DEP 0.988 0.300 3.64e-1 8.31 19 1.09e+1 7.91 5.59
## 46 Taiga Flycat… ARR -0.722 0.250 3.05e-1 6.93 19 8.35e+0 6.60 5.46
## 47 Tufted Duck DEP 0.511 0.447 9.13e-2 7.48 13 1.31e+0 6.96 6.28
## 48 Tufted Duck ARR -0.700 0.527 1.19e-1 8.82 13 1.76e+0 8.21 6.67
## 49 Western Yell… DEP 0.0612 0.241 2.93e-3 8.50 22 6.46e-2 8.14 6.13
## 50 Western Yell… ARR -1.73 0.204 7.65e-1 7.22 22 7.15e+1 6.91 5.48
## # ℹ 1 more variable: CV <dbl>RMSE, MAE, and RSE make the most sense. Using thresholds of 20, 20, and 25 respectively, here is a summary of our example species that passed or failed wrt ARRIVAL timings.
## # A tibble: 25 × 9
## COMMON.NAME SLOPE SE RSE RMSE MAE RSE.PASS RMSE.PASS MAE.PASS
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <lgl> <lgl> <lgl>
## 1 Bar-headed Goose -0.129 0.146 4.95 4.74 3.83 TRUE TRUE TRUE
## 2 Bar-tailed Godwit -0.997 0.958 8.33 7.21 5.37 TRUE TRUE TRUE
## 3 Black Redstart -0.409 0.172 3.96 3.74 2.90 TRUE TRUE TRUE
## 4 Blyth's Reed War… -3.33 0.459 15.6 14.9 11.0 TRUE TRUE TRUE
## 5 Booted Eagle -0.976 0.209 5.38 5.11 3.69 TRUE TRUE TRUE
## 6 Brown Shrike -0.732 0.160 5.42 5.19 3.77 TRUE TRUE TRUE
## 7 Brown-breasted F… -1.78 1.02 15.6 14.4 8.60 TRUE TRUE TRUE
## 8 Brown-headed Gull -1.04 0.533 14.9 14.1 10.6 TRUE TRUE TRUE
## 9 Cinereous Vulture -2.39 2.38 27.1 24.5 17.6 FALSE FALSE TRUE
## 10 Common Buzzard 0.480 0.335 8.08 7.56 5.58 TRUE TRUE TRUE
## 11 Common Chiffchaff -1.22 0.440 8.88 8.34 6.35 TRUE TRUE TRUE
## 12 Eurasian Wigeon -1.35 0.272 9.81 9.39 7.30 TRUE TRUE TRUE
## 13 Gray Wagtail 0.342 0.209 5.38 5.10 4.07 TRUE TRUE TRUE
## 14 Greater Spotted … 0.0515 0.332 12.0 11.5 8.01 TRUE TRUE TRUE
## 15 Green Warbler -1.78 0.270 5.44 5.11 3.92 TRUE TRUE TRUE
## 16 Greenish Warbler -0.980 0.280 8.32 7.94 6.29 TRUE TRUE TRUE
## 17 Lesser Whitethro… -0.610 0.255 8.13 7.76 6.39 TRUE TRUE TRUE
## 18 Pallid Harrier -1.62 0.240 6.43 6.10 5.03 TRUE TRUE TRUE
## 19 Red-breasted Fly… -0.642 0.248 7.39 7.05 6.05 TRUE TRUE TRUE
## 20 Siberian Stonech… -0.705 0.182 4.35 4.10 3.04 TRUE TRUE TRUE
## 21 Spotted Redshank 0.552 1.02 30.9 29.4 22.4 FALSE FALSE FALSE
## 22 Sykes's Warbler -1.51 0.984 21.5 20.2 17.3 TRUE FALSE TRUE
## 23 Taiga Flycatcher -0.722 0.250 6.93 6.60 5.46 TRUE TRUE TRUE
## 24 Tufted Duck -0.700 0.527 8.82 8.21 6.67 TRUE TRUE TRUE
## 25 Western Yellow W… -1.73 0.204 7.22 6.91 5.48 TRUE TRUE TRUE
Figure 10: Comparisons of different measures of variability for arrival timings.
It is evident that RMSE is the most susceptible to single, large-deviance points pulling away the overall measure. It also seems that MAE might be the most appropriate for us: aside from Dunlin and Pied Harrier (which are treated similarly by all three), all other remove species have been clustered tightly and separated from the species we want to retain.
Let us check whether this is true for departure timings as well. Here, the best thresholds are 14, 10 and 15 respectively for RMSE, MAE and RSE.
## # A tibble: 25 × 9
## COMMON.NAME SLOPE SE RSE RMSE MAE RSE.PASS RMSE.PASS MAE.PASS
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <lgl> <lgl> <lgl>
## 1 Bar-headed Goose 1.26 0.283 9.58 9.17 7.31 TRUE TRUE TRUE
## 2 Bar-tailed Godwit 3.89 2.60 22.6 19.6 14.7 FALSE FALSE FALSE
## 3 Black Redstart 2.21 0.292 6.72 6.34 5.27 TRUE TRUE TRUE
## 4 Blyth's Reed War… 1.86 0.213 7.21 6.90 5.77 TRUE TRUE TRUE
## 5 Booted Eagle -0.0444 0.250 6.45 6.12 4.95 TRUE TRUE TRUE
## 6 Brown Shrike 0.519 0.282 9.55 9.14 6.49 TRUE TRUE TRUE
## 7 Brown-breasted F… 2.47 0.479 7.30 6.72 5.03 TRUE TRUE TRUE
## 8 Brown-headed Gull -0.766 0.472 13.2 12.5 9.69 TRUE TRUE TRUE
## 9 Cinereous Vulture 6.21 0.921 10.5 9.48 8.07 TRUE TRUE TRUE
## 10 Common Buzzard -0.272 0.880 21.2 19.9 14.1 FALSE FALSE FALSE
## 11 Common Chiffchaff 1.46 0.410 8.28 7.78 6.10 TRUE TRUE TRUE
## 12 Eurasian Wigeon 0.795 0.344 12.4 11.9 8.88 TRUE TRUE TRUE
## 13 Gray Wagtail 0.425 0.253 6.52 6.18 5.05 TRUE TRUE TRUE
## 14 Greater Spotted … 0.245 0.254 9.16 8.79 6.80 TRUE TRUE TRUE
## 15 Green Warbler 0.363 0.467 9.43 8.86 7.02 TRUE TRUE TRUE
## 16 Greenish Warbler -0.459 0.362 10.8 10.3 8.83 TRUE TRUE TRUE
## 17 Lesser Whitethro… 1.50 0.462 14.7 14.1 10.9 TRUE FALSE FALSE
## 18 Pallid Harrier 0.0227 0.334 8.96 8.50 7.00 TRUE TRUE TRUE
## 19 Red-breasted Fly… 1.53 0.312 9.28 8.85 6.69 TRUE TRUE TRUE
## 20 Siberian Stonech… 1.39 0.246 5.86 5.52 4.50 TRUE TRUE TRUE
## 21 Spotted Redshank 0.504 0.327 9.96 9.45 7.35 TRUE TRUE TRUE
## 22 Sykes's Warbler 0.147 0.847 18.5 17.3 13.1 FALSE FALSE FALSE
## 23 Taiga Flycatcher 0.988 0.300 8.31 7.91 5.59 TRUE TRUE TRUE
## 24 Tufted Duck 0.511 0.447 7.48 6.96 6.28 TRUE TRUE TRUE
## 25 Western Yellow W… 0.0612 0.241 8.50 8.14 6.13 TRUE TRUE TRUE
Figure 11: Comparisons of different measures of variability for departure timings.
RMSE seems like a poor option again. MAE is again decent, but this time RSE is also good. Need to see how values for species change with updated 2024 data.
The number of species that pass and fail each criterion are:
## # A tibble: 6 × 5
## DATE.TYPE CRITERION FAIL PASS PASS.PROP
## <fct> <chr> <int> <int> <dbl>
## 1 DEP MAE.PASS 35 55 0.611
## 2 DEP RMSE.PASS 26 64 0.711
## 3 DEP RSE.PASS 27 63 0.7
## 4 ARR MAE.PASS 7 83 0.922
## 5 ARR RMSE.PASS 12 78 0.867
## 6 ARR RSE.PASS 9 81 0.9